Several international, regional and national standards have been developed to define methods and systems that may be used to implement multichannel audio coding systems. Three examples of such standards include ISO/IEC 13818-7, Advanced Audio Coding (AAC), also known as “MPEG-2 AAC,” and ISO/IEC 14496-3, subpart 4, also known as “MPEG-4 audio,” published by the International Standards Organization (ISO), and a standard published by the United States Advanced Television Systems Committee (ATSC), Inc. in Document A/52B entitled “Digital Audio Compression Standard (AC-3, E-AC-3),” Revision B, published Jun. 14, 2005, also known as “Dolby Digital” or “AC-3.”
Audio systems that conform to standards like those mentioned above generally include transmitters that apply an analysis filterbank to each of several channels of input audio signals, process the output of the analysis filterbanks into encoded signals and transmit or record the encoded signals, and receivers that receive the encoded signals, decode them and apply synthesis filterbanks to the decoded signals to generate channels of output audio signals that are a replica of the original input audio signals. Many of the standards specify implementing the analysis and synthesis filterbanks by a Modified Discrete Transform (MDCT) and an Inverse Modified Discrete Transform (IMDCT) described in Princen, Johnson, and Bradley, “Subband/Transform Coding Using Filter Bank Designs Based on Time Domain Aliasing Cancellation,” ICASSP 1987 Conf. Proc., May 1987, pp. 2161-64.
Filterbanks that are implemented by these particular transforms have many attractive properties but significant processing or computational resources are required to perform the needed calculations. Techniques are known that can be used to perform the transforms more efficiently, thereby reducing the amount of computational resources that are needed. One characteristic that is common to these techniques is that their computational complexity varies with the so-called length of the transform. Techniques are known that can realize further reductions in computational complexity by using shorter transform lengths to process audio channels with narrower bandwidths.
Standards like those mentioned above define sequences of digital data or digital bit streams that carry data representing encoded representations of one or more audio channels. One configuration of channels sometimes referred to as “5.1 channels” includes five full-bandwidth channels denoted left (L), right (R), center (C), left-surround (LS), and right-surround (RS), and one limited-bandwidth channel or low-frequency-effects (LFE) channel. The full-bandwidth channels typically have a bandwidth of about 20 kHz and the limited-bandwidth LFE channel typically has a bandwidth of about 100 to 200 Hz. Because the bandwidth of the LFE channel is narrower, known techniques can be used to perform a filterbank transform more efficiently for the LFE channel than can be performed for one of the full-bandwidth channels.
Nevertheless, there is a need to develop techniques that further improve the efficiency of the transform filterbanks that are applied to limited-bandwidth channels like the LFE channel.